6301 (Discrete Mathematics for Computer Scientists)
... Course Description and Objectives This is a first year course for Computer Scientists, introducing students to material they will need in future computer science courses and providing basic tools for problem solving. Topics covered include: set theory, equivalence relations, functions, symmetry grou ...
... Course Description and Objectives This is a first year course for Computer Scientists, introducing students to material they will need in future computer science courses and providing basic tools for problem solving. Topics covered include: set theory, equivalence relations, functions, symmetry grou ...
12 How to Compute the SVD
... An improvement over the Golub-Kahan algorithm is given by the Lawson-HansonChan algorithm. Its operations count is approximately 2mn2 + 2n3 which is more efficient if m > 35 n. The main idea for the Lawson-Hanson-Chan algorithm is to first compute a QR factorization of A, i.e., A = QR. Then one appl ...
... An improvement over the Golub-Kahan algorithm is given by the Lawson-HansonChan algorithm. Its operations count is approximately 2mn2 + 2n3 which is more efficient if m > 35 n. The main idea for the Lawson-Hanson-Chan algorithm is to first compute a QR factorization of A, i.e., A = QR. Then one appl ...
The smallest eigenvalue of a large dimensional Wishart matrix
... { having a density with positive support on [(1 - tF)',(l + ,F>t], and when yi r, { yieldsadditionalmasson {0}. It is also known fGeman (1980)]that the maximum eigenvalueI(** of M" convergesa.s. to (1 + ,F)'as s -+ oo. [The statement of thi. r"rult in Geman (1980) has all the M, constructedfrom one ...
... { having a density with positive support on [(1 - tF)',(l + ,F>t], and when yi r, { yieldsadditionalmasson {0}. It is also known fGeman (1980)]that the maximum eigenvalueI(** of M" convergesa.s. to (1 + ,F)'as s -+ oo. [The statement of thi. r"rult in Geman (1980) has all the M, constructedfrom one ...
Computational Linear Algebra
... Press QUIT (2nd MODE) to go back to the standard calculator screen. If we want to enter a matrix name on the screen, go back to the MATRIX screen (2nd x-1) and select the name you want. Note this screen tells you which matrices have values and their sizes. Press ENTER and the name will appear on the ...
... Press QUIT (2nd MODE) to go back to the standard calculator screen. If we want to enter a matrix name on the screen, go back to the MATRIX screen (2nd x-1) and select the name you want. Note this screen tells you which matrices have values and their sizes. Press ENTER and the name will appear on the ...
3.5 Perform Basic Matrix Operations
... Augmented Matrices II..Augment = to enhance, to make something bigger. A) Augmented matrix = a linear system written as a single matrix. 1) ax + by = # a b # a b # cx + dy = # ...
... Augmented Matrices II..Augment = to enhance, to make something bigger. A) Augmented matrix = a linear system written as a single matrix. 1) ax + by = # a b # a b # cx + dy = # ...
Using Matrices to Perform Geometric Transformations
... this will make the triangle smaller. If you dilate by a factor ½, the triangle will be half as big as it originally was. You can investigate this on your own. ...
... this will make the triangle smaller. If you dilate by a factor ½, the triangle will be half as big as it originally was. You can investigate this on your own. ...
Square Roots and Adjacency Matrices
... Question 1.1. Can you place 4 points in the plane such that any two points are an odd distance apart? 2. Last Week’s HW Average was about 90/100 – consequently, there wasn’t much to really talk about. Most students seemed to be comfortable with the basic concepts; however, there was some confusion i ...
... Question 1.1. Can you place 4 points in the plane such that any two points are an odd distance apart? 2. Last Week’s HW Average was about 90/100 – consequently, there wasn’t much to really talk about. Most students seemed to be comfortable with the basic concepts; however, there was some confusion i ...
Möbius Transformations
... variable. So if we want to find the real part of (M ′ (z))2 , which is what we will need to for the series approximation, we will have to do some complex-number simplification. ...
... variable. So if we want to find the real part of (M ′ (z))2 , which is what we will need to for the series approximation, we will have to do some complex-number simplification. ...
Solving systems of 3x3 linear equations using a TI
... Solving systems of 3x3 linear equations using a TI-84 plus and matrices. Solve the system: x − 2 y + 3z = 0 ...
... Solving systems of 3x3 linear equations using a TI-84 plus and matrices. Solve the system: x − 2 y + 3z = 0 ...
(1)
... (d) how many free variables does this system of equations have? (e) write down the solutions of this equation system. 2. Perform each operation, or state that the operation is impossible. ...
... (d) how many free variables does this system of equations have? (e) write down the solutions of this equation system. 2. Perform each operation, or state that the operation is impossible. ...